A primary concern of geophysical research has become the problem of distinguishing reliably between gas, oil and water in situ by acoustic means, as well as inferring the relative mineral concentration and the rock type, and the rock porosity and permeability. That is, if oil, gas or water is present in a given rock formation it is important to determine whether it can be extracted therefrom; i.e., the permeability or "connectedness" of the porous structure of the rock layer, which permits the gas or oil to be pumped out, is critical.
It is known that the acoustic velocity in liquid saturated porous rock can differ substantially from that in the same rock where a free gaseous phase is partially present. Two such layers in contact can thus account for a large reflection coefficient to an acoustic wave. However, the dependence of acoustic velocity on gas saturation is very weak in the range between 10 and 90 percent saturation, and hence is a poor quantitative measure of economic value of the minerals present.
Unpublished work indicates that a potentially more sensitive parameter to gas saturation is acoustic wave attenuation. It has been reported that the attenuation of an acoutic wave in a gas sand, for example, is at least twice that in a water sand. That is supported by theoretical work by Mavko et al, "Wave Attenuation in Partially Saturated Rocks" Geophysics, Vol. 44(2) p. 161 (1969), where it is demonstrated that the presence of both a gas and a liquid phase in pores is far more attenuating to seismic excitation than are pores fully saturated with either.
It has recently been demonstrated that attenuation is an order of magnitude more sensitive to saturation than is velocity and that partially saturated, fully saturated and dry rocks can be distinguished from one another by the relative attenuation of compressional and shear modes of vibration in the frequency range of 500 Hz to a few kHz. See Winkler et al, "Friction and Seismic Attenuation Rocks", Nature, 277 p. 528 (1979). Thus, in principle, attenuation could serve as an independent data point useful in determining the state of saturation of porous rocks as well as the identification of the lithology.
Seismic attenuation is often expressed in terms of the so-called "quality factor" Q. Q is usually defined as the maximum energy stored during a single cycle of sinusoidal deformation divided by the energy lost during the cycle. When the loss is large, however, this definition breaks down. It has instead been suggested that Q be defined in terms of the mean stored energy, W, and the energy loss, .DELTA.W, during a single cycle: ##EQU1## When this definition is used, Q is related to the phase angle between stress and strain .delta. by: EQU tan .delta.=1/Q
It has previously been suggested by Kjartansson that Q may be assumed to be frequency independent and that measurements of the attenuation of acoustic wave forms in rock layers may be suitable to provide an indication of Q. See Kjartansson, "Models for Frequency Dependent Q", Stanford Rock Physics Progress Report, 5, p. 88 (1978). The present inventors have found, however, that simple measurement of the attenuation of wave forms is not sufficient to measure Q regardless of whether Q is frequency independent. The best results possible with this method merely provide a value for Q in the single layer case, that is, in which Q is constant over the area of travel of the acoustic wave. Such a monolayer is not of substantial interest in lithologic studies, in which it is the locations of and lithology between the interfaces between various rock layers which are of geologic significance and which are sought to be detected. Accordingly, a method of determining Q in areas where the rock structure changes rapidly, as is frequently the case in formations of interest, is required.